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**A Note on Generalizing the Savage-Dickey Density Ratio**

**Isabella Verdinelli and Larry Wasserman**

### Abstract:

*We present a simple method for computing Bayes factors. The method
derives from observing that, in general, a Bayes factor can be written
as the product of a quantity called the ``Savage-Dickey density
ratio'' and a correction factor; both terms are easily estimated from
posterior simulation. In some cases, it is possible to do these
computations without ever evaluating the likelihood, in contrast to
some other methods.
**
**KEY WORDS AND PHRASES:* Bayes factor, hypothesis testing, Markov
chain Monte Carlo.